1 00:00:08,240 --> 00:00:10,220 Welcome back to 8.701. 2 00:00:10,220 --> 00:00:14,120 In this lecture, we'll talk about CP symmetry 3 00:00:14,120 --> 00:00:17,680 or CP violation. 4 00:00:17,680 --> 00:00:19,420 In previous lectures, we discussed 5 00:00:19,420 --> 00:00:23,710 that the weak interaction is not invariant under parity 6 00:00:23,710 --> 00:00:25,930 and charge conjugation transformation. 7 00:00:25,930 --> 00:00:29,500 But now we can ask the question, how about CP-- 8 00:00:29,500 --> 00:00:33,550 so transformation which does change conjugation and parity 9 00:00:33,550 --> 00:00:35,140 transformation. 10 00:00:35,140 --> 00:00:37,930 The classical example to show parity violation 11 00:00:37,930 --> 00:00:40,250 is the decay of a pion. 12 00:00:40,250 --> 00:00:45,660 So we have here this charge pion with spin 0. 13 00:00:45,660 --> 00:00:49,270 And it decays into a muon and a neutrino, an anti-muon 14 00:00:49,270 --> 00:00:50,590 and a neutrino. 15 00:00:50,590 --> 00:00:56,180 And so since the neutrino is left-handed, the-- 16 00:00:56,180 --> 00:00:58,700 [INAUDIBLE] decay coming onto muon 17 00:00:58,700 --> 00:01:01,500 needs to be left-handed as well. 18 00:01:01,500 --> 00:01:04,190 So if you do parity transformation of this decay, 19 00:01:04,190 --> 00:01:08,270 you see that the outcoming muon would be right-handed. 20 00:01:08,270 --> 00:01:11,750 On the other hand, there is no right-handed neutrino. 21 00:01:11,750 --> 00:01:14,950 And therefore, this decay is not possible. 22 00:01:14,950 --> 00:01:16,350 So this is not-- 23 00:01:16,350 --> 00:01:19,590 so this mirror symmetry is not realized in nature, 24 00:01:19,590 --> 00:01:22,350 as a consequence of the weak interaction. 25 00:01:22,350 --> 00:01:25,290 So similarly, we could do a charge transformation, a charge 26 00:01:25,290 --> 00:01:28,070 conjugation, of this decay. 27 00:01:28,070 --> 00:01:30,930 So you turn particles into the antiparticles. 28 00:01:30,930 --> 00:01:34,140 And you find here this antineutrino, 29 00:01:34,140 --> 00:01:35,100 which is left-handed. 30 00:01:35,100 --> 00:01:37,350 And also, those don't exist in nature. 31 00:01:37,350 --> 00:01:40,590 So parity or charge conjugation doesn't really 32 00:01:40,590 --> 00:01:43,230 work on those decays, those [INAUDIBLE] decays. 33 00:01:43,230 --> 00:01:46,980 But what does work, if you apply the parity and a charge 34 00:01:46,980 --> 00:01:52,860 conjugation, we turn the positively-charged pion 35 00:01:52,860 --> 00:01:57,750 into a negatively-charge pion, the antimuon into a muon, 36 00:01:57,750 --> 00:02:00,240 and the neutrino into an antineutrino. 37 00:02:00,240 --> 00:02:05,440 And you see here that the antineutrino is right-handed. 38 00:02:05,440 --> 00:02:07,110 So is the muon. 39 00:02:07,110 --> 00:02:10,850 And so that decay is actually observed in nature. 40 00:02:10,850 --> 00:02:11,690 Good. 41 00:02:11,690 --> 00:02:13,640 So we saved the day. 42 00:02:13,640 --> 00:02:18,140 It seems like that CP, that the weak interaction 43 00:02:18,140 --> 00:02:21,410 is invariant in the CP transformation. 44 00:02:21,410 --> 00:02:25,640 However, that's not quite true. 45 00:02:25,640 --> 00:02:32,210 Gell-Mann and Pais noted that in systems of neutral kaons, 46 00:02:32,210 --> 00:02:33,480 there's an artifact. 47 00:02:33,480 --> 00:02:36,410 And the fact is that a particle, a K0, 48 00:02:36,410 --> 00:02:42,550 can turn into an antiparticle by changing the strangeness. 49 00:02:42,550 --> 00:02:47,770 And that's possible in this kind of box diagrams, 50 00:02:47,770 --> 00:02:51,460 which include a box with a couple of W's. 51 00:02:54,400 --> 00:03:00,340 And it's easy to see that if you could prepare a kaon, 52 00:03:00,340 --> 00:03:03,640 it will oscillate, because those diagrams are possible, 53 00:03:03,640 --> 00:03:05,920 into an antiparticle. 54 00:03:05,920 --> 00:03:10,150 So now what is happening now to CP here, 55 00:03:10,150 --> 00:03:15,080 if I apply CP on a kaon, I find a minus sign and an antikaon. 56 00:03:15,080 --> 00:03:17,080 So if you want to analyze this further, 57 00:03:17,080 --> 00:03:19,760 you might want to find the eigenstates to this. 58 00:03:19,760 --> 00:03:22,570 And so the eigenstates can be found, as well as K1 59 00:03:22,570 --> 00:03:28,860 and K2, which are admixtures of the K0 and the anti-K0. 60 00:03:28,860 --> 00:03:31,360 And you find this symmetric, the symmetric 61 00:03:31,360 --> 00:03:33,530 and the anti-symmetric states. 62 00:03:33,530 --> 00:03:34,460 Good. 63 00:03:34,460 --> 00:03:37,300 So if you apply CP on the eigenstates, 64 00:03:37,300 --> 00:03:41,170 you find eigenvalues of 1 and minus 1. 65 00:03:41,170 --> 00:03:46,630 It turns out that the lifetime of decay 1 decay 2, 66 00:03:46,630 --> 00:03:50,350 those eigenstates, is very different. 67 00:03:50,350 --> 00:03:53,080 One is 10 to the minus 10, and one is 5 times 10 68 00:03:53,080 --> 00:03:54,550 to the minus 8. 69 00:03:54,550 --> 00:03:58,990 So decay 1 decays much, much quicker than decay 2. 70 00:03:58,990 --> 00:04:03,860 So this, then, sets the stage to a test of CP violation. 71 00:04:03,860 --> 00:04:08,500 So what you're going to do is prepare a beam of K0's and let 72 00:04:08,500 --> 00:04:10,990 them decay. 73 00:04:10,990 --> 00:04:14,470 And only after some time, you study the beam again, 74 00:04:14,470 --> 00:04:18,850 which then should be made up solely of K2's. 75 00:04:18,850 --> 00:04:22,330 So if you in that beam observe decays of the K2 76 00:04:22,330 --> 00:04:28,270 into two pions, you noted that there is an admixture again, 77 00:04:28,270 --> 00:04:30,520 which violates CP. 78 00:04:30,520 --> 00:04:34,450 So you have an admixture of K1's in a beam which should just be 79 00:04:34,450 --> 00:04:36,220 of K2's. 80 00:04:36,220 --> 00:04:41,500 So that mixture, then, will violate CP invariance. 81 00:04:41,500 --> 00:04:43,630 And exactly that was done. 82 00:04:43,630 --> 00:04:46,360 So Croning and Fitch picked up this idea. 83 00:04:46,360 --> 00:04:50,230 They set up an experiment in which they produced kaons. 84 00:04:50,230 --> 00:04:51,520 They had them decay. 85 00:04:51,520 --> 00:04:53,800 And then they studied later in the beam 86 00:04:53,800 --> 00:04:57,370 whether or not they could find two pion decays. 87 00:04:57,370 --> 00:05:00,264 And they did, indeed, observe 42-- 88 00:05:00,264 --> 00:05:08,840 45 pion decays, two-pion decays, in a total of 22,700 decays. 89 00:05:08,840 --> 00:05:13,570 So that means that this K long beam, the long-lived kaon beam, 90 00:05:13,570 --> 00:05:18,310 is actually an admixture of K2's with a small additional 91 00:05:18,310 --> 00:05:20,710 component of K1's. 92 00:05:20,710 --> 00:05:26,450 So here they observed CP violation 93 00:05:26,450 --> 00:05:30,020 through the mixture of those states. 94 00:05:30,020 --> 00:05:32,340 And this epsilon gives you, you know, 95 00:05:32,340 --> 00:05:37,770 size of the strength of the CP violation. 96 00:05:37,770 --> 00:05:39,480 So here is a note of the paper. 97 00:05:39,480 --> 00:05:41,790 We'll have another discussion of this in class 98 00:05:41,790 --> 00:05:44,970 by a student presentation, Croning and Fitch. 99 00:05:44,970 --> 00:05:48,150 Here this is Croning, and this is Fitch. 100 00:05:48,150 --> 00:05:53,010 It turns out that Croning is actually a student, 101 00:05:53,010 --> 00:05:55,200 or was a student, of Enrico Fermi and also 102 00:05:55,200 --> 00:05:57,460 worked in Chicago. 103 00:05:57,460 --> 00:05:59,370 So that's quite an interesting family tree 104 00:05:59,370 --> 00:06:03,900 here, to which also Jerry Friedman belongs. 105 00:06:03,900 --> 00:06:07,320 Jerry Friedman is a retired faculty at MIT 106 00:06:07,320 --> 00:06:10,060 and discovered that protons are made out of quarks. 107 00:06:10,060 --> 00:06:12,130 So this is a very interesting family tree. 108 00:06:12,130 --> 00:06:14,472 If you have some time, you might want to look into this. 109 00:06:14,472 --> 00:06:15,555 But here's the experiment. 110 00:06:15,555 --> 00:06:18,630 So you take protons, you dump them into a beam. 111 00:06:18,630 --> 00:06:24,270 You try to, with this magnet, filter out a neutral component, 112 00:06:24,270 --> 00:06:28,800 get rid of all photons, and then let this beam decay, 113 00:06:28,800 --> 00:06:32,280 and look in the spectrometer for decays of two photons. 114 00:06:32,280 --> 00:06:34,690 Here's a bigger picture of the same spectrum. 115 00:06:34,690 --> 00:06:37,680 So this is actually a blow-up view of this. 116 00:06:37,680 --> 00:06:41,820 So you have your kaons, neutral kaons coming in, the K2's. 117 00:06:41,820 --> 00:06:44,790 And then you look for pion decays. 118 00:06:44,790 --> 00:06:47,820 The instrumentation and how we actually would do this 119 00:06:47,820 --> 00:06:50,190 is part of later discussions where we actually talk 120 00:06:50,190 --> 00:06:54,740 about detectors in more detail. 121 00:06:54,740 --> 00:06:55,780 All right. 122 00:06:55,780 --> 00:07:00,310 So we just saw that Croning and Fitch observed CP violation 123 00:07:00,310 --> 00:07:02,590 in mixture of states. 124 00:07:02,590 --> 00:07:06,500 But we can also observe CP violation in direct decays. 125 00:07:06,500 --> 00:07:09,505 And the classical example here is the case of the K 126 00:07:09,505 --> 00:07:11,730 long and semileptonic decays. 127 00:07:11,730 --> 00:07:15,250 So semileptonic here means we have a decay of the K long, 128 00:07:15,250 --> 00:07:18,670 a neutral particle and a charged pion, an electron 129 00:07:18,670 --> 00:07:20,350 and antineutrino-- 130 00:07:20,350 --> 00:07:26,080 or it might very well also decay into a pi minus, a positron, 131 00:07:26,080 --> 00:07:27,610 and a neutrino. 132 00:07:27,610 --> 00:07:31,750 And it turns out, when you really count those events 133 00:07:31,750 --> 00:07:34,570 and perform a precise experiment, 134 00:07:34,570 --> 00:07:37,660 that the K longs prefer decays to positrons 135 00:07:37,660 --> 00:07:39,700 over decays to electrons. 136 00:07:39,700 --> 00:07:42,850 And so the fractional amount of this imbalance 137 00:07:42,850 --> 00:07:45,730 is 3 times 10 to the minus 3. 138 00:07:45,730 --> 00:07:48,850 So this is a rather small effect, again, of CP violation 139 00:07:48,850 --> 00:07:52,420 here in direct decays. 140 00:07:52,420 --> 00:07:54,370 Since then, CP violation has also 141 00:07:54,370 --> 00:07:57,130 been shown in the decay of B mesons. 142 00:07:57,130 --> 00:07:59,320 And the program of studying B mesons 143 00:07:59,320 --> 00:08:04,510 is a big part of the LHC experiment at the LHC. 144 00:08:04,510 --> 00:08:07,520 There's also experiments in Japan going on right now 145 00:08:07,520 --> 00:08:14,380 which study B mesons in order to learn further about B systems. 146 00:08:14,380 --> 00:08:16,360 Tests are also underway, for those 147 00:08:16,360 --> 00:08:19,310 who listened to the colloquium on Monday, in the neutrino 148 00:08:19,310 --> 00:08:20,170 sector. 149 00:08:20,170 --> 00:08:22,510 So here we have a completely different part, 150 00:08:22,510 --> 00:08:26,350 so not quarks are involved in weak interaction but neutrinos. 151 00:08:26,350 --> 00:08:28,060 And so the question is whether or not 152 00:08:28,060 --> 00:08:32,159 in that sector of physics, that sector of the standard model, 153 00:08:32,159 --> 00:08:34,150 there is CP violation. 154 00:08:34,150 --> 00:08:36,820 Those are aspects we'll discuss later on when we talk 155 00:08:36,820 --> 00:08:40,270 about neutrinos specifically. 156 00:08:40,270 --> 00:08:46,380 Before I close, a few more remarks 157 00:08:46,380 --> 00:08:51,130 on the matter-antimatter symmetry. 158 00:08:51,130 --> 00:08:54,540 So one of the biggest mysteries in physics, I would claim, 159 00:08:54,540 --> 00:08:58,000 is the fact that we're even here to ask this question. 160 00:08:58,000 --> 00:09:00,090 So there is apparently more matter 161 00:09:00,090 --> 00:09:02,070 in the universe than antimatter. 162 00:09:02,070 --> 00:09:04,620 You start from a big bang, there was this symmetry, 163 00:09:04,620 --> 00:09:08,080 and now we live in a universe which is dominated by matter. 164 00:09:08,080 --> 00:09:10,120 So how is this possible? 165 00:09:10,120 --> 00:09:15,570 So in 1967, Zakharov proposed that this 166 00:09:15,570 --> 00:09:20,230 is possible in a system where baryon number is violated. 167 00:09:20,230 --> 00:09:21,930 So this is almost a trivial statement. 168 00:09:21,930 --> 00:09:23,400 If you start from an equal number 169 00:09:23,400 --> 00:09:27,300 of baryons and antibaryons, the sum is then 0. 170 00:09:27,300 --> 00:09:29,940 The baryon number is 0 of this system. 171 00:09:29,940 --> 00:09:32,880 And you end up in a system which is dominated by baryons, 172 00:09:32,880 --> 00:09:36,030 then baryon number needs to be violated. 173 00:09:36,030 --> 00:09:39,040 But there's also the need of CP violation in this. 174 00:09:39,040 --> 00:09:43,470 So we just saw that this is realized in nature. 175 00:09:43,470 --> 00:09:46,560 But the amount of CP violation we observe in the system I just 176 00:09:46,560 --> 00:09:49,830 discussed is not sufficient to explain 177 00:09:49,830 --> 00:09:52,830 the matter-antimatter symmetry we observe in nature. 178 00:09:52,830 --> 00:09:54,150 So there is more to be found. 179 00:09:54,150 --> 00:09:59,250 There's new physics to be looked for in CP violation 180 00:09:59,250 --> 00:10:00,780 on this overall question. 181 00:10:00,780 --> 00:10:04,740 And there's also a need for the actions 182 00:10:04,740 --> 00:10:06,840 to be out of equilibrium, meaning 183 00:10:06,840 --> 00:10:10,225 that you don't revert the processes as you go forward. 184 00:10:13,660 --> 00:10:16,540 Yet another point of discussion, which I will not 185 00:10:16,540 --> 00:10:19,030 go into much detail in this lecture, 186 00:10:19,030 --> 00:10:22,870 is that our quantum field theory, which 187 00:10:22,870 --> 00:10:25,750 describes quasi-standard model and describes 188 00:10:25,750 --> 00:10:29,360 the interaction of particles, is invariant, 189 00:10:29,360 --> 00:10:32,290 and the CPT transformations. 190 00:10:32,290 --> 00:10:35,110 That means that if CP is violated, 191 00:10:35,110 --> 00:10:39,170 time reversal cannot be a symmetry. 192 00:10:39,170 --> 00:10:41,350 So meaning, going backwards and forwards in time 193 00:10:41,350 --> 00:10:43,600 is not symmetric. 194 00:10:43,600 --> 00:10:44,690 And you can test this. 195 00:10:44,690 --> 00:10:48,980 You can design experiments which test [INAUDIBLE] the fact. 196 00:10:48,980 --> 00:10:52,840 You can also design experiments which test CPT directly. 197 00:10:52,840 --> 00:10:55,090 But this is-- those are all interesting questions, 198 00:10:55,090 --> 00:10:59,810 but we will not go into any of those in this lecture. 199 00:10:59,810 --> 00:11:02,260 We will, however, come back to understanding 200 00:11:02,260 --> 00:11:05,500 the origin of CP violation in the standard model when 201 00:11:05,500 --> 00:11:11,470 we talk in more detail about the weak interaction.